an:03870440
Zbl 0546.62057
Monnez, J. M.
Convergence of a general stochastic approximation process under convex constraints and some applications
EN
Mathematical learning models - theory and algorithms, Proc. Conf., Bad Honnef/Ger. 1982, Lect. Notes Stat. 20, 156-167 (1983).
1983
a
62L20 62J02 60F15
convex constraints; martingales; separable Hilbert space
[For the entire collection see Zbl 0517.00013.]
A general stochastic approximation process (s.a.p.) in a closed convex subset of a separable Hilbert space is considered and a.s. convergence is proved. The results include as special cases the \textit{D. Ruppert}'s dynamic s.a.p. [Ann. Stat. 7, 1179-1195 (1979; Zbl 0427.62059)], \textit{L. Ljung}'s s.a.p. with correlated observations [ibid. 6, 680-696 (1978; Zbl 0402.62060)], as well as \textit{A. E. Albert} and \textit{L. E. Gardner}'s s.a.p.'s for estimating regression models [Stochastic approximation and nonlinear regression. (1967; Zbl 0162.215)]. The presentation is rather short, details being given in the author's Ph. D. dissertation, Universit?? de Nancy I (1982).
R.Zielinski
Zbl 0517.00013; Zbl 0427.62059; Zbl 0402.62060; Zbl 0162.215